Abstract
We review some aspects of three-dimensional quantum gravity with emphasis in
the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal
algebra. The general solution to the classical equations of motion with anti-de
Sitter boundary conditions is displayed. This solution is parametrized by two
functions which become Virasoro operators after quantisation. A map from the
space of states to the space of classical solutions is exhibited. Some recent
proposals to understand the Bekenstein-Hawking entropy are reviewed in this
context. The origin of the boundary degrees of freedom arising in 2+1 gravity
is analysed in detail using a Hamiltonian Chern-Simons formalism.
